vector modelling of hydrating cement microstructure and kinetics cement.pdf

8/20/2019 Vector modelling of hydrating cement microstructure and kinetics cement.pdf

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POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES

PAR

M.Eng. in civil engineering, University of Tokyo, Japonet de nationalité indienne

acceptée sur proposition du jury:

Prof. P. Muralt, président du juryProf. K. Scrivener, directrice de thèse

Dr R. Flatt, rapporteurProf. A. Nonat, rapporteur

Prof. M. Rappaz, rapporteur

Vector Modelling of Hydrating Cement

Microstructure and Kinetics

Shashank BISHNOI

THÈSE NO 4093 (2008)

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

PRÉSENTÉE LE 5 JUIN 2008

À LA FACULTE SCIENCES ET TECHNIQUES DE L'INGÉNIEUR

LABORATOIRE DES MATÉRIAUX DE CONSTRUCTION

PROGRAMME DOCTORAL EN SCIENCE ET GÉNIE DES MATÉRIAUX

Suisse2008


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Abstract

A new modelling framework, called μic, has been developed to enable

simulations of complex particulate growths, in particular the microstructural

evolution of hydrating cement paste. μic has been developed using the vector

approach, which preserves the multi-scale nature of the cement microstructure.

Support libraries built into the framework enable fast simulation of systems

containing millions of particles, allowing every single particle in a system to be

modelled and all the interactions to be calculated. The modelling framework has

been developed using obect oriented programming and its extensible and flexible

architecture, due to this microstructural development mechanisms and algorithms

can be easily added. The framework facilitates the otherwise complex task of

modelling new systems and phenomena. The microstructures generated by μic canbe used to obtain important information that can in the future be used to model

the evolution of mechanical properties and durability-related phenomena. The

model can also be used to study the mechanisms of microstructural development of

cement.

!arious models of cement hydration kinetics and the reaction mechanism

were tested using μic. "t was observed that while the traditional approach to the

nucleation and growth mechanism could be used to explain the acceleration of

reaction-rates during the early hydration of cement pastes, the subse#uent

deceleration could not be reproduced. "f a diffusion controlled mechanism is used

to explain the deceleration, changes larger than an order of magnitude in the

transport properties of $-S-% have to be assumed. &urthermore, the rate of change

of reaction rates shows a continuous linear evolution through the reaction peak

and the thickness around different particle si'es would be very different at the

onset of the supposed diffusion regime. "t was found that it is possible to explain

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the hydration kinetics during the first () hours using a nucleation and growth

mechanism when a loosely packed $-S-% with a lower bulk density is assumed to

form. "t is proposed that this loosely packed $-S-% fills a large fraction of the

microstructure within a few hours of hydration and that its density continues toincrease due to an internal growth process within the bulk of the product. "t was

found that an initial density of $-S-% between *.+ gcc and *.( gcc was re#uired

in order to fit the observed experimental behaviour. hile this density is much

lower than the generally accepted range of +. gcc to (.+ gcc, this low packing

density can explain the absence of water in large capillary pores observed in /01

measurements that study cement hydration on wet samples, and the fibrous or

ribbon-like nanostructure of $-S-% observed in high-resolution T20 images.

The current study demonstrates the versatility of μic and how the possibilityof modelling different phenomena on a multi-scale three-dimensional model can

prove to be an important tool to achieve better understanding of cement

hydration. "t was also shown that the use of mechanistic, rather than empirical,

rules can improve the predictive power of the models.

3ey ords4 0icrostructure, 0odelling, 0odelling platform, !ector approach,

$ement, Alite, %ydration, 3inetics, 0echanism, $alcium silicatehydrate, 5ensification

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Résumé

6ne nouvelle architecture d7di7e 8 la mod7lisation ayant pour nom μic a 7t7

d7velopp7e pour permettre la simulation de ph7nom9nes de croissance particulaire

complexes, en particulier l:7volution micro-structurelle de la p;te de ciment au

cours de son hydratation. mes.

5iff7rents mod9les de cin7ti#ue d:hydratation du ciment et de m7canismes de

r7action ont 7t7 test7s avec


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du $-S-% autour de particules de tailles diff7rentes serait tr9s variable au moment

du changement de r7gime. "l est possible d:expli#uer la cin7ti#ue d:hydratation

durant les premi9res () heures en utilisant un m7canisme de nucl7ation et

croissance si l:on suppose la formation d:un $-S-% peu dense. "l est propos7 #ue ce$-S-% peu dense remplisse une importante part de la microstructure lors des

premi9res heures de l:hydratation, puis #ue sa densit7 augmente par le moyen d:un

processus de croissance interne. "l a 7t7 trouv7 #ue la densit7 initiale devait >tre

entre *.+ gcc et *.( gcc pour reproduire le comportement exp7rimental observ7.

uoi#ue cette densit7 soit tr9s inf7rieure au bornes g7n7ralement accept7es,

comprises entre +. gcc et (.+ gcc, elle peut expli#uer l:absence d:eau dans les

grands pores capillaires observ7e lors d:7tudes utilisant la 10/ sur des

7chantillons en condition humide, ainsi #ue la nanostructure fibreuse en rubans du$-S-% observ7e sur des images 02T 8 haute r7solution.

$ette 7tude d7montre la versatilit7 de me mod9le multi-

7chelle tri-dimensionnel, comme outil permettent une meilleure compr7hension de

l:hydratation du ciment. "l est 7galement montr7 #ue l:usage de r9gles de nature

m7caniste plut@t #u:empiri#ue am7liore le pouvoir pr7dictif des mod9les.

0ots $l7s4 0icrostructure, 0od7lisation, Architecture de mod7lisation,

Approche vectorielle, $iment, Alite, %ydratation, $in7ti#ue,

07canisme, Silicate de calcium hydrat7, 5ensification

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Acknowledgement

" would like to express my gratitude to all the people who helped me over the

last three and a half years in the work leading to this dissertation. &irstly " would

like to thank my supervisor Brof. 3aren Scrivener for giving me the opportunity to

work with her, for the regular Cat times heatedD discussions, for being a constant

source of motivation Cand at times annoyanceD and most of all for being a great

boss and an even greater sport from the first to the last day of this work. " thank

2B&= for accepting me as a student and supporting me with a scholarship for the

first year of the Bh.5. " thank the Swiss /ational Science &oundation for providing

financial support for this research.

Thanks to all my colleagues at =0$ for the all the great work and fun.

Special thanks to my office mates 0ohsen and Eulien for all the great times Cand

stupid pranksD, to $yrille, the encyclopaedia of all useful Cand lots more pointlessD

information, for all the stimulating discussions, to 3yle for bringing the much

needed practical perspective Cand prudishnessD. Thanks to 5r. /avi and 5r. Bignat

for letting me work on their model and explaining its details. Thanks to 0ercedes

for letting me steal her experimental results and alite, and to 2mmanuel for

philosophising about these results. Thanks to Amor for the discussions. To all

=0$ colleagues for their invaluable help and support. Also thanks to all the

different people who were willing to discuss my work during workshops, seminars

and weekdays.

0y love and thanks to my loving, caring and patient Cand at times pesteringD

wife 1uchi for getting me through all the rough and the smooth, for always being

there and supporting me no matter what, for being my best friend. Thanks to my

parents for giving me the motivation to work and the freedom and support to be

myself.

V


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Table of Contents

Abstract....................................................................................................i

Résumé....................................................................................................iii

Acknowledgement....................................................................................v

Table of Contents...................................................................................vii

List of Tables...........................................................................................xi

List of Figures........................................................................................xiii

Glossary.................................................................................................xix

Chapter ! "ntroduction...........................................................................+

Chapter #! Cement $ydration! Chemistry and %umerics.......................F(.+ Broduction, $omposition and %ydration of $ement......................F(.( %ydration of Alite..........................................................................

(.(.+ 0odels of $-S-%......................................................................(.(.( 5istribution of %ydrates........................................................++

(.G %ydration 3inetics of $ement......................................................+)

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(.) Stages of Alite %ydration.............................................................+F(.).+ Stages + H (4 5issolution and "nduction Beriods..................+I(.).( Stage G4 Accelerating 1eaction 1ates....................................+(.).G Stages ) H F4 1educing 1eaction 1ates................................+J

(.F Analytical and /umerical 0odels of %ydration 3inetics.............(*(.F.+ $oncentric Krowth 0odels....................................................(*(.F.( The Eohnson-0ehl-Avrami-3olmogorov 2#uation................(G(.F.G The 5ion /umerical 0odel for Loundary /ucleation.........(I

(.I Summary of $ement %ydration and Mutstanding uestions.......(N(. 0odelling $ement %ydration.......................................................G*

(..+ /umerical 0odels for $ement 0icrostructure......................GG(..( =imitations of $urrently available 0odels............................)G

(.N $urrent Study...............................................................................))

Chapter &! 'ic the (odel.......................................................................)FG.+ hy a 0icrostructural 0odel......................................................)FG.( 1e#uirements from μic..................................................................)

G.(.+ 2xtensibility..........................................................................)G.(.( 2ase of 5evelopment.............................................................)NG.(.G 0ulti-scale 0icrostructural 1epresentation..........................)NG.(.) Berformance...........................................................................)JG.(.F Accessibility...........................................................................)J

G.G The !ector Approach...................................................................)JG.G.+ Bossible Assumptions in !ector Approach...........................F(

G.G.( !ector Approach as 6sed in μic............................................FGG.G.G Algorithms for a &aster !ector Approach.............................F

G.) 0odelling $ement %ydration.......................................................I(G.).+ 0aterials and 1eactions........................................................I)G.).( $ement Barticles...................................................................I)G.).G 1eaction 3inetics..................................................................IIG.).) 5istribution of 0aterials.......................................................IG.).F 5ensity !ariation..................................................................IG.).I 0echanisms of 0icrostructural 2volution............................ING.). Specific orkarounds............................................................IJ

G.).N Blugins...................................................................................+G.).J An 2xample Broblem definition............................................(G.F Mutput from the 0odel................................................................I

Chapter )! *imulating (icrostructures using 'ic...................................J).+ Traditional 0icrostructural Simulations4 Barticle-Si'es..............J

).+.+ 0echanisms and 1ules..........................................................N*).+.( The Simulations.....................................................................NG).+.G Approximate Bore-Si'e 5istributions....................................NF

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).+.) Mbservations and 5iscussion.................................................NI).( /on-Traditional 2xamples with μic.............................................N

).(.+ 0echanisms and 1ules..........................................................N).(.( The Simulations.....................................................................NJ

).(.G 1esults...................................................................................J*).(.) 5iscussion..............................................................................J+

).G $onclusions...................................................................................J(

Chapter +! %ucleation and Growth ,inetics of Alite.............................JGF.+ "ntroduction..................................................................................JGF.( /umerical 0odelling of 1eaction 3inetics...................................J)

F.(.+ 1e#uirements from /umerical 0odels of 3inetics................J)F.(.( 6sing 2xperimental 1esults in $onunction with 0odels.....J)

F.G The Avrami 2#uation...................................................................JIF.G.+ A Simplified 5erivation of the Avrami 2#uation..................JF.G.( =imitations of the Avrami 2#uation.....................................JN

F.) Simulating the /ucleation and Krowth 0echanism...................+*+F.).+ %omogeneous /ucleation and Krowth................................+*(F.).( %eterogeneous /ucleation and Krowth...............................+*FF.).G 1esults.................................................................................+*N

F.F 2xperimental "nvestigations into %ydration 3inetics................++*F.F.+ Avrami &its of $urves.........................................................++(F.F.( 1ate of Acceleration............................................................++GF.F.G 2ffect of "nert &illers...........................................................++F

F.F.) Summary of 2xperimental 1esults......................................++F.I 3ey uestions before 0odelling Alite %ydration.......................++N

F.I.+ "nduction Beriod..................................................................++NF.I.( Accelerating Stage...............................................................++J

F. 0odelling Traditional /ucleation and Krowth in μic................+(+F..+ 3inetics................................................................................+(GF..( &it Barameters and 1esults.................................................+(FF..G 5iscussion............................................................................+(

F.N 2xistence of a 5iffusion $ontrolled 1egime...............................+G*F.N.+ Simulations with a 5iffusion $ontrolled 0echanism..........+G*

F.N.( 1ate of $hange of %ydration 3inetics................................+GGF.N.G 5ependence of 1eaction 1ate on %ydrate Thickness..........+GFF.J $-S-% with Age-5ependent 5ensity...........................................+GI

F.J.+ 3inetics................................................................................+GIF.J.( &it Barameters and 1esults.................................................+GJF.J.G 5iscussion............................................................................+)(

F.+* Simulating the &iller 2ffect......................................................+))F.++ 5eductions from the Simulations..............................................+)IF.+( 5iscussion..................................................................................+)F.+G $onclusions...............................................................................+F*

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Chapter -! Conclusions and erspecti/es.............................................+FGI.+ 0icrostructural 0odelling and μic.............................................+FGI.( %ydration 3inetics......................................................................+F)I.G Berspectives on 0icrostructural 0odelling................................+FF

I.) Berspectives on %ydration 3inetics............................................+F

References.............................................................................................+FJ

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List of Tables

Table (.+4 Abbreviations in cement science...............................................................I

Table (.(4 $ontents of Bortland cement...................................................................I

Table G.+4 $alculation of bounding x values of spheres...........................................FJ

Table G.(4 Mrder of particles in the bounding box list along x axis from data intable G.+..................................................................................................FJ

Table G.G4 Summary of improvements in the vector approach................................I(

Table F.+4 Barameters used in the homogeneous nucleation and growth simulations..............................................................................................................+*(

Table F.(4 Barameters used in the heterogeneous nucleation and growthsimulations............................................................................................+*I

Table F.G4 5etails of the powders and fit parameters with the Avrami e#uation. +++

Table F.)4 $alculated and measured specific surface Cm(kgD using differenttechni#ues and measured slope of the #uasi-linear part of the heat-evolution CmghD.............................................................................++)

Table F.F4 Barameters used in uniform density nucleation and growth simulations..............................................................................................................+(F

Table F.I4 Barameters used in Avrami e#uation and diffusion e#uation simulations..............................................................................................................+G+

Table F.4 Barameters used in variable density nucleation and growth simulations..............................................................................................................+)(

Table F.N4 5etails of simulations with densifying $-S-%.......................................+)(

Table F.J4 Barameters used in simulations to study the filler effect.....................+)F

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List of Figures

&igure (.+4 The &eldman-Sereda model of $-S-%+, the circles show adsorbed waterand crosses show inter-layer water...........................................................N

&igure (.(4 Schematics of low-density CleftD and high-density CmiddleD $-S-%according to Eennings model(*, and the modified globular unit((..............J

&igure (.G4 S20 micrograph of $GS hydrating in paste Cfrom de Eong et al.(GDC=eftD, and T20 micrograph showing low-density fibrillar outer andinner $-S-% in a mature cement paste Cfrom 1ichardson(D C1ightD.......J

&igure (.)4 Transmission electron micrograph of low-density product inside theshell Cfrom 0athur()D. Bores are in black and materials in lighter tonesin this dark-field image...........................................................................+*

&igure (.F4 T20 image of inner product in a hardened cement paste resembling a

colloidal suspension of fibres Cfrom 1ichardson(ID..................................+*&igure (.I4 5rawing of cement microstructure for *.G wc having a capillary

porosity of OGG. Spaces marked :$: represent capillary pores...............+(

&igure (.4 2volution of a hydrating cement grain Cafter Scrivener))D...................+G

&igure (.N4 Typical heat evolution curve of Bortland cement.................................+)

&igure (.J4 Typical heat evolution curve of the alite phase....................................+F

&igure (.+*4 Schematic representation of hydrating $GS grain in concentric growthmodels by 3ondo and 6edaGN CleftD and Bommersheim and $lifton)J

CrightD.....................................................................................................(*&igure (.++4 Schematics of overlapping spherical grains from AvramiI..................(G

&igure (.+(4 Schematics of the nucleation and growth implemented in the 5ionmodel......................................................................................................(

&igure (.+G4 1elationship of compressive strength with gel-space ratio CafterBowers +JFNJD..........................................................................................G+

&igure (.+)4 2xperimental scatter of compressive strengths of different systemsagainst Lalshin:s modelJ(........................................................................G+

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&igure ).)4 0icrostructures at FO hydration for BS5-+ CleftD, BS5-( CmiddleD andBS5-G CrightD, with $GS in lightest grey-scale, followed by $% and $-S-% and pores in black...............................................................................NF

&igure ).F4 2rosion to identify pore-skeleton using pixels Cthe solids are shown inblackD......................................................................................................NF

&igure ).I4 Bore si'e distribution at FO and JFO degree of hydration.................NI

&igure ).4 Schematics for normal CleftD and branching growth CrightD..................NN

&igure ).N4 2xample of step-wise addition of spheres in branching growth............NJ

&igure ).J4 2volution of the microstructure with non-branching fibres with solid-volume fraction of +G.GO CleftD, ((.O CmiddleD and G(.*O CrightD.......J*

&igure ).+*4 2volution of the microstructure with branching fibres with solid-volume fraction of .+O CleftD, G+.FO CmiddleD and IF.O CrightD.........J*

&igure ).++4 2volution of the volume filled by solids with normal and branchingfibres.......................................................................................................J+

&igure ).+(4 1ate of reaction with non-branching CleftD and branching CrightD fibres................................................................................................................J+

&igure F.+4 5ependence of reaction rates predicted by the Avrami e#uation on kand n .......................................................................................................JJ

&igure F.(4 &raction of volume filled CleftD and rate of filling CrightD for the first setof simulations........................................................................................+*G

&igure F.G4 Snapshots of slices from the first set of simulations, with fraction ofvolume occupied approximately GIO CleftD and J*O CrightD................+*G

&igure F.)4 &it of simulations +-LL and )-ML with the Avrami e#uation............+*)

&igure F.F4 5ifferent perpendicular and vertical growth rates from spherical nuclei..............................................................................................................+*I

&igure F.I4 5egree of reaction CleftD and rate of reaction CrightD for the second setof simulations........................................................................................+*

&igure F.4 Three-dimensional snapshots from simulations I-LL CleftD and -L5CrightD....................................................................................................+*

&igure F.N4 Lest fits of the Avrami e#uation with results from simulations I to N..............................................................................................................+*N

&igure F.J4 Barticle si'e distributions of different fractions of alite.......................++*

&igure F.+*4 1ate of heat evolution for alite fractions A, L, $, 2 and &..............++(

&igure F.++4 1ate of heat evolution for alite fractions A, 5 and K.......................++(

&igure F.+(4 &its of the Avrami e#uation with three fractions without an inductionperiod....................................................................................................++G

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&igure F.+G4 1enormalised specific fineness: of powders against measured slopes.++)

&igure F.+)4 Barticle si'e distributions of alite and fillers used.............................++I

&igure F.+F4 %eat evolution from samples with alite replaced by rutile................++I

&igure F.+I4 %eat evolution from samples with alite replaced by silica fume........++

&igure F.+4 %eat evolution curve as a sum of exponential decay and Avramie#uation with and without an induction period...................................++J

&igure F.+N4 2volution of heat-flow measured by isothermal calorimetry CleftD andsurface area measured by /01 relaxometry CrightD by Raac+(I..........++J

&igure F.+J4 Schematics of the nucleation and growth mechanism with differentparallel and outwards growth rates for a single particle CtopD andbetween particles CbottomD...................................................................+(G

&igure F.(*4 $omparison between simulations and experimental results of heat-evolution rates and degrees of hydration..............................................+(I

&igure F.(+4 A slice from the simulation of fraction &-+F μm at the peak. The poresare shown in black, alite in dark-grey and hydrates in white..............+(N

&igure F.((4 5egree of hydration against rate of reaction for calculations andexperiments...........................................................................................+(N

&igure F.(G4 $omparison between simulations and experimental results of heat-evolution rates and degrees of hydration..............................................+G(

&igure F.()4 %eat-rates and differential of heat-rates for the fractions and

calculated from the Avrami e#uation, as marked.................................+G)&igure F.(F4 5ependence of the rate of hydration on the approximate thickness of

products................................................................................................+GI

&igure F.(I4 Schematics of the nucleation and growth mechanism with differentparallel and outwards growth rates and densification of the product fora single particle CtopD and between particles CbottomD........................+GN

&igure F.(4 $omparison between simulations and experimental results of heat-evolution rates and degrees of hydration for simulations with variabledensity of product.................................................................................+)*

&igure F.(N4 5ependence of simulated heat-evolution on parameters for fraction2-+N μm.................................................................................................+)+

&igure F.(J4 !ariation of k 2 with the number of particles per unit volume in thesimulations............................................................................................+)+

&igure F.G*4 A slice from fraction L-NG μm close to the peak, with pore-space inblack, anhydrous grains in dark grey and hydrates in white................+))

&igure F.G+4 $alculated rates of heat-evolution from simulations with inert fillers..............................................................................................................+)F

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&igure F.G(4 5egree of hydration against the rate of heat-evolution from differentalite samples with and without fine filler particles...............................+)J

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Glossary

Abbre/iations

L2T4 Lrunauer, 2mmett and Teller theory

LS24 Lack-Scattered 2lectrons

$A4 $ellular Automata

$%T4 $ement %ydration Tool-kit

$!4 $omputational !olume

&204 &inite 2lement 0ethod

"B304 "ntegrated Barticle 3inetics 0odelE534 Eava 5evelopment 3it

E!04 Eava !irtual 0achine

/014 /uclear 0agnetic 1esonance

MB$4 Mrdinary Bortland $ement

BS54 Barticle Si'e 5istribution

2/S4 uasi-2lastic /eutron Scattering

12!4 1epresentative 2lementary !olume

S204 Scanning 2lectron 0icroscopy

T204 Transmission 2lectron 0icroscopy

wc4 ater to $ement 1atio

Cement chemistry notation

$4 $aM

S4 SiM(

%4 %(M

A4 Al(MG

&4 &e(MG

S4 SMG

$GS4 Tricalcium Silicate$(S4 5icalcium Silicate

$GA4 Tricalcium Aluminate

$)A&4 Tetracalcium Aluminoferrite

$-S-%4 $alcium Silicate %ydrate

$%4 $alcium %ydroxide

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Chapter 1 !ntroduction

This study presents a new modelling platform called μic Cpronounced 0ikeD.

This platform uses the vector approach in three-dimensions to model the

microstructural development of hydrating cement pastes. μic uses the vector

approach to represent the geometry of the microstructure. The efficiency of the

vector approach was improved in order to enable simulations of millions of

particles with the calculation of all interactions in the system. 5ue to its flexible

design, the users of the platform can define custom materials, particles and

reactions, and control the development of the microstructure by defining laws that

define the mechanisms of the reactions. The versatility of μic allows users to model

many different particulate growth systems not limited to cement hydration.

"n this study the modelling platform has been used to model various possible

hydration mechanisms and the applicability of these mechanisms has been tested

by comparison with experimental results. The hydration kinetics of alite samples

with different particle si'e distributions were simulated. The calculated results

were compared against heat-evolution from hydrating alite samples measured using

isothermal calorimetry. The results provide important information regardingcement hydration and highlight the gaps in our understanding of the underlying

mechanisms.

Mne of the maor problems in studying cement is the large number of

interactions at work during hydration. This interaction happens between different

materials and different particles at the same time. As most of these processes occur

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Introduction

at the micro-scale, they cannot be directly observed and indirect experimental

techni#ues are used to study them. &or example, while calorimetry is widely usedto study the rate of hydration of cement, since only the total heat-evolved from

samples is measured, the individual reaction rates of individual phases are not

available. Similarly, while electron microscopy is widely used to study the

evolution of cement microstructures, since most of the high-resolution techni#ues

re#uire a drying of the sample, the progress of hydration on the same sample

cannot be observed.

Since most of our understanding of the mechanism of cement hydrationdepends on various indirect experimental techni#ues, the results are often open to

interpretation. hile most experimental techni#ues provide bulk-values of the

properties, the underlying mechanisms occur at the micrometre or nanometre scale,

interpretation of the link between mechanisms and properties re#uires

simplifications regarding interactions which are difficult to test. %owever, with the

continuous development of computational techni#ues, it has now become possible

to numerically simulate these processes and to observe their macroscopic effects,which can be compared with experimental results.

/umerical models use combinations of fundamental processes to simulate

systems and processes. The processes underlying these models generally define the

behaviour of smaller discrete sub-systems and the interactions between these sub-

systems. Since smaller and simpler elements of the system are considered, the

behavioural laws are much simpler to formulate analytically and the task of

integration of the behaviour of the entire system is left to the computer. /umerical

models can, therefore, be used as an important techni#ue, which works in a way

complimentary to the experiments, in order to further our understanding of cement

hydration.

Still, most of the currently available numerical models on cement remain

empirical and highly dependent on experimental results. hile this is not

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Chapter 1: Introduction

surprising, given the wide range of parameters on which the properties of cements

depend, these models can only serve a limited purpose in the advancement of ourunderstanding of the processes underlying cement hydration. 2mpirical models are

mathematical expressions that are designed to follow the experimental results and

do not necessarily represent the mechanisms that control these properties. 2ven if

used only for predicting properties for different conditions, empirical models are

only applicable over a limited range of conditions and are hard to extend beyond

this range.

&or these reasons, the need for a numerical microstructural model which canincorporate customised mechanisms in simulations was felt. μic provides a

modelling platform on which different theories concerning cement hydration could

be explicitly modelled and studied. At the same time, μic provides an effective

means to reconstruct numerical microstructures resulting from complex processes

that occur at the level of individual particles. These microstructures can be

analysed for the calculation of different properties, such as mechanical and

transport properties in the case of cement.

The following chapters discuss the importance of numerical modelling in

cement science, the development of μic and its features, and numerical studies of

cementitious systems using μic. $hapter ( discusses our current understanding of

cement hydration and different approaches used thus far to understand and model

hydration and microstructural development. !arious microstructural models and

their advantages and drawbacks are also presented in this chapter.

$hapter G presents the concepts behind the development of μic and its

architecture. The typical procedure for defining a problem in μic has also been

presented.

$hapter ) demonstrates that while μic can be used to simulate hydrating

cement microstructures using the traditionally applied laws on customary set-ups,

it can also be used to model other, completely different, systems. "t has also been

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Introduction

shown that microstructural models can be used to obtain both, the localised effects

of bulk properties and the macroscopic effects of microscopic mechanisms."n chapter F, μic has been used to investigate hydration kinetics of alite.

1ates of hydration measured from alite powders with different particle si'e

distributions have been compared with computed results obtained from the

simulation of different hydration mechanisms. "t has been shown that some of the

widely accepted mechanisms cannot explain the hydration kinetics of alite and new

explanations of the observed behaviour are needed.

$hapter I presents the conclusions of the study and the perspectives for

future numerical and experimental studies on cement hydration.

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Chapter " Cement #ydration Chemistry

and $umerics

"n this chapter, our current state of knowledge of cement hydration and theapproaches used to understand it further and to model it are presented. "n the

discussion, some of the important aspects of hydration that are still not well

understood are identified. "t is seen that, while cement science has evolved

considerably over the last century, many important aspects of hydration are still

not well understood. hile many advances have been made in modelling cement

hydration, most of the existing models rely heavily on empirical results, often

limiting the applicability of the models. Since the current work deals with alitehydration, the hydration of alite will be focussed upon in the following discussion.

2.1 Productio! Co"#o$itio %d H&dr%tio o' C("(t

Bortland cement is produced by burning lime, clay and other naturally

available minerals mixed in a kiln in large amounts at around +)F*$+. The

materials partially fuse to form clinker nodules upon cooling. $linker is chiefly

composed of phases containing calcium oxide, silicon dioxide, aluminium oxide andferric oxide, present with other minority components such as magnesium,

potassium and sodium oxides. The nodular clinker is then mixed with a small

#uantity Ctypically around FOD of calcium sulphate and is finely ground to produce

cement.

5


28/190

Production, Composition and Hydration of Cement

&or the sake of convenience, the names of most of the constituents of cement

are abbreviated, as listed in table (.+. The oxides in the clinker combine to formphases that constitute cement. &or example, calcium oxide and silicon dioxide

combine to form a modified form of tricalcium silicate, which is also known as alite

and is the most important phase in cement. The other maor phases present in

cement are belite, aluminate and ferrite Ctable (.(D. The phases are not present in

their pure form and contain ionic substitutions in their crystalline structures.

$alcium sulphate is added to the clinker before grinding. Although typically

referred to as gypsum, other forms of calcium sulphate may also be used.Table 2.1: Abbreviations in cement science

For"u)% A**r(+i%tio For"u)% A**r(+i%tio

CaO C SiO2 S

Al2O3 A Fe2O3 F

MgO M K2O K

SO3 S H2O H

Table 2.2: Contents of Portland cement Co"#oud P,%$( N%"($ A**r(+i%t(d N%"( Tic%) %"out

Tricalcium Silicate Alite C3S 50-70

!icalcium Silicate "elite C2S 15-30

Tricalcium Alumi#ate Alumi#ate C3A 5-10

Tetracalcium Alumi#$%errite Ferrite C4AF 5-15

$ement reacts with water in a process called hydration. ith hydration, the

solid volume in cement paste increases, converting cement into a stiff solid. The

reaction products, called hydrates, give cement its binding properties and are

responsible for strength development. "n the following sections, the hydration of

cement, and particularly alite, the development of its microstructure and its

reaction kinetics are discussed in more detail.

&


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Chapter 2: Cement Hydration: Chemistry and Numerics

2.2 H&dr%tio o' A)it(

Alite reacts with water producing calcium silicate hydrate C$-S-%D andcalcium hydroxide C$% or portlanditeD, as shown in e#uation (.+.

$GSF.G%$

+.S%

)+.G$% C(.+D

This e#uation is not always exact as the composition of $-S-% is known to

vary(,G,). Still, $+.S%) is currently assumed to be an acceptable approximation for

the product+. Bortlandite is crystalline in nature and has a well-defined

composition. "t is known to grow either as massive crystals or as hexagonal

platelets, depending on the pore-solution and cement compositionF,I,. "n Bortland

cement, belite also hydrates in a manner similar to alite, producing similar

products, as shown in e#uation (.(. Lelite reacts only to a small extent in the early

ages, and acts as a reserve for hydration at later agesN.

$(S).G%$+.S%)*.G$% C(.(D

ithin a few hours of mixing with water, cement paste starts to gain in

stiffness and strength, going from a viscous fluid to a plastic solid to a stiff solidJ.This change happens because the hydration products have a lower density than

the anhydrous phases and occupy more space, filling most of the space created by

the consumption of water and increasing the solid volume. $-S-% is the most

important hydration product as it fills the largest amount of space in a hydrated

cement and holds the microstructure together. A large number of studies on the

development of cement microstructure, therefore, focus on the properties of $-S-%.

2.2.1 Mod()$ o' C-S-H

The $-S-% in cement is often classified into inner and outer product. The $-

S-% that occupies the space created by the dissolution of alite is usually referred to

as the inner product and the $-S-% that grows in the space between the particles

is called the outer productJ. The values of the bulk density of $-S-% in the

7


30/190

Hydration of Alite

literature vary, mostly between +.NF gcc and (.+ gcc+*,++,+(,+G. hile values ofporosity of $-S-% found in the literature vary between (NO and )JO J,+), it is

generally accepted that inner $-S-% has a lower porosity than the outer $-S-%.

The solid density of $-S-% has been reported to be between (.F gcc and

(.N gcc+),+F,+I.

There is general agreement on the development of a porous, gel-like, higher-

density inner and a lower-density outer product, although the structure of $-S-% is

still not clear and several models of $-S-% exist. &eldman and Sereda+,+N postulated

a layered structure of $-S-% with water bonded between the layers of $-S-% and

also adsorbed on the surface of the layers Cfigure (.+D. This model was based on

nitrogen sorption and the observed length and modulus changes in samples at

different moisture conditions. 5aimon et al.+J made similar conclusions based on

nitrogen and water-vapour absorption and made minor modifications to the model.

Lased on surface-area and shrinkage measurements using different techni#ues,

Eennings presented a colloidal structure for $-S-%(*,(+, which is similar to the

Bowers model in many aspectsJ. According to this model, $-S-% exists as a fractal

assembly of spherical globules, that are arranged in different configurations that

control its density and the presence of two types of $-S-% was suggested (* Cfigure

(.(D. The variable density of $-S-% has been proposed in many earlier studies as

wellJ,+*. "n a later modification, the spherical globules were replaced by layered

'

Figure 2.1: The Feldman-Sereda model of C-S- 1! " the circles sho# adsorbed #ater andcrosses sho# inter-la$er #ater


31/190


bricks, although they are still referred to as globules, in order to explain large

irreversible changes resulting from shrinkage and creep((.

Although the exact chemical structure of $-S-% is not known, it is often

compared to that of ennite and tobermoriteG,(F. The molecular structure of $-S-%

is beyond the scope of the current study, but it is noteworthy that $-S-% has

generally been attributed with a layered chain structure with short-range

crystallinityG,(F,(. This structure also manifests at the sub-micron-scale as in

microscopic studies $-S-% has been described as a platy or fibrousG,I,(G,(N,(. A

(

Figure 2.2: Schematics of lo#-densit$ %left& and high-densit$ %middle& C-S- according to'ennings model 2( " and the modified globular unit 22

Figure 2.): S*+ microgra,h of C ) S h$drating in ,aste %from de 'ong et al.2) & %eft&" andT*+ microgra,h sho#ing lo#-densit$ fibrillar outer and inner C-S- in a mature cement

,aste %from ichardson 2! & %ight&


32/190

Hydration of Alite

fibrillar $-S-% can be seen in many published micrographs Cfigures (.G and (.)D

and images resembling suspensions of fibrillar or foil-like $-S-% can also be found.

The fibrous structure of $-S-% has often been used to explain the

development of mechanical properties in cementI,(G,(N,(. "t has been argued that the

fibrous structures grow outwards from cement particles and get tangled, or oin

with the fibres from the other particles giving cement its mechanical propertiesI,+N,(N.

The microstructure of $-S-% is still not well understood. All models of $-S-%

suffer from different weaknesses and none of them can explain all observed

10

Figure 2./: T*+ image of inner ,roduct in a hardened cement ,aste resembling acolloidal sus,ension of fibres %from ichardson 20 &

Figure 2.: Transmission electron microgra,h of lo#-densit$ ,roduct inside the shell%from +athur 2&. Pores are in black and materials in lighter tones in this dark-field image.


33/190


properties. Lut until the formation of $-S-% cannot be directly observed as it

occurs, our understanding of its structure can only be limited to extrapolativeinterpretations of indirect experimental measurements.

2.2.2 Di$tri*utio o' H&dr%t($

The main problem in understanding the development of cement

microstructure lies in the fact that all the important processes in hydration happen

on the microscopic scale and cannot be observed directly. A combination of various

techni#ues have traditionally been used to study the hydration of Bortland cementand many different theories regarding the mechanism of hydration and the

structure of hydrates have been presented.

"n their pioneering work on the development of cement microstructure in

+J)*s, Bowers and Lrownyard(J presented a systematic study of cement hydration

and the development of properties of cement paste. Although their experiments

were largely limited to observed macroscopic phenomena, the theories postulated

extended into the nano-scale. The authors carried out wide ranging experimentsmeasuring properties such as compressive strength, bleeding rate, length-changes

and weight loss due to drying and presented an extensive set of theories on the

development of properties of concrete and cement. Some of the ideas presented in

their work are still used practicallyG*,G+,G(.

"n their study, cement microstructure was presented as a collection of

spherical gel hydrate particles collecting around cement particles, leaving empty

spaces which were called the capillary pores. A denser inner product, which

constitutes around )FO of the total product, forms inside the original boundaries

of the grains and a lower density outer product fills the space outside, binding the

grains together. The inner product grows inwards and the outer product outwards

from the original grain boundaries.

11


34/190

Hydration of Alite

The gel was suggested to contain a water-filled porosity in the vicinity of (N

percent by volume and the water in these pores was referred to as the non-

evaporable water. The spherical particles of gel were later replaced by ribbon-like

fibres in line with microscopic observations. A drawing of the modified model is

shown in figure (.I. Bowers also used this model to explain the mechanical and

frost-resistance properties of concreteJ,G),GF.

The Bowers model of cement microstructure was originally developed before

high resolution electron micrographs of cement were available, but later

microscopic observations reinforced and improved many of the ideas presented. &or

example, the spherical gel particles in the Bowers model were replaced by ribbon-

like fibresJ in line with electron micrographs presented by KrudemoGI,G, who was

one of the first to study the microstructure of cement paste using electron

microscopy. hile there were some discrepancies between the early observations,

most studies agreed with the growth of an outer product away from the grain and

an inner product towards the hydrating particlesI,GN,GJ,)*. "t was noted that no clear

boundary between the inner and outer products was apparent)*.

hile the microstructure can be affected due to sample processing before

microscopic observations, the micrographs still provide important information

about the development of the microstructure. %adley)+ observed the presence of

shells of hydrates around cement grains, at a small distance, in S20 images of

12

Figure 2.0: ra#ing of cement microstructure for (.) #3c having a ca,illar$ ,orosit$ of!4 )) . S,aces marked 5C5 re,resent ca,illar$ ,ores.


35/190


36/190

Hydration of Alite

"t must be noted here that most samples for electron microscopy go through

extensive preparation, usually involving drying, fracturing or polishing andimpregnation in resin, which could alter the microstructure. Still electron

microscopy is a powerful means to study processes that may otherwise not be

visible.

2. H&dr%tio Ki(tic$ o' C("(t

5ifferent phases of cement react at different and time-varying rates. As

cement hydration is exothermic in nature, heat evolution measured by calorimetryis an effective method of following the overall progress of hydration. &igure (.N

shows the typical heat evolution curve recorded using an isothermal calorimeter

during approximately the first day of hydration of ordinary Bortland cement. The

curve is broadly divided into five stages.

The first stage gives a rapid evolution of heat for several minutes. This is

generally attributed to the initial rapid dissolution of cement particles and a rapid

hydration of the aluminate phase)N. A continuous low evolution of heat is observedin the second stage of the process. This stage is referred to as the induction period

or the dormant period and, although the mechanism behind this period is disputed,

14

Figure 2.6: T$,ical heat evolution curve of Portland cement


37/190


it is apparent that there is some barrier to reaction before it picks up again in the

next stage. "n stage three, the reaction accelerates for a few hours before a peak isreached. The heat evolution subsides in the following hours in stage four and

settles to a more constant value in stage fiveGN,)J,F*.

At any stage of hydration, the observed heat evolution might be the result of

a combined reaction of more than one cement phase and it is difficult to isolate the

contribution of individual phases. Although these phases might behave in a

different way in isolation than in the presence of other phases in cement, studies

on pure cement phases have provided valuable information about the reactionmechanism and kinetics of each phase in cement. Since alite, the primary phase in

cement, is focussed upon in this study, the hydration of alite is discussed in more

detail in the following discussion.

2./ St%0($ o' A)it( H&dr%tio

&igure (.J shows the typical heat evolution curve from the hydration of alite.

As shown in the figure. the curve can be divided into five main stages, thecommonly used names of which are listed below4

• Stage +4 5issolution period,

15

Figure 2.7: T$,ical heat evolution curve of the alite ,hase


38/190

Stages of Alite Hydration

• Stage (4 "nduction period,

•Stage G4 Acceleration period,

• Stage )4 5eceleration period, and

• Stage F4 Slow reaction.

2./.1 St%0($ 1 2 Di$$o)utio %d Iductio P(riod$

A large evolution of heat, generally attributed to the rapid dissolution of $GS,

which rapidly subsides within a few minutes, is observed in the first stage of the

curve

GN

. "t has been shown that the rate of dissolution in this stage depends on theparticle si'e, crystalline structure and defects of $GSF+,F(. =eading into the second

stage, the rate of reaction slows-down considerably before a saturation with respect

to the anhydrous phases is reached)N and it has been proposed that the dissolution

slows down due to saturation with respect to $-S-%FG. "t has also been suggested

that the reaction slows down due to the formation of a meta-stable layer of

hydrates around the reacting particlesGN,F).

The second stage witnesses a much lower heat evolution that can last forover an hour. 5espite this stage being often referred to as the dormant period, a

continuous heat-evolution is observed in this stage. This indicates that the reaction

continues at a slow rate during this period.

The mechanism behind the second stage has long been a subect of debate.

Bossibly due to the shape of the evolution during the first two stages, which looks

similar to the dissolution of salts nearing saturation, the induction period was at

first attributed to saturation with respect to the anhydrous phasesFF, but this was

#uickly reected as evidence indicated much lower concentrations in the solution)N.

The formation of an inhibiting or protective layer of early hydrates around the

reacting particles, which is later breached, was suggested to slow down the

reaction during the induction periodF),FI,F,FN.

1&


39/190


3ondo and 6edaGN, and later Bommersheim and $lifton)J, presented the

mechanism of early hydration of cement using mathematical models, where theinduction period was explained by the formation of a protective layer on the

surface of the particles and the subse#uent acceleration was explained by the

gradual erosion of this layer. These models are discussed in more detail in section

(.F.+. "t was also suggested that calcium ions tend to dissolve faster than the

silicate ions upon the initial hydrolysis of $GS immediately after mixing with water

and the adsorption of these calcium ions on the silica-rich surface layer could lead

to a slow-down in the dissolution of $GSFJ

. Still, no conclusive evidence of thepresence of any inhibiting layer has been reported and most arguments in its

favour are speculative.

The poisoning of $% crystals by SiM( has also been suggested to cause the

induction periodFJ,I*. "t has however been shown using dilute solutions of alite that

the nucleation of portlandite can be repressed until the accelerating part of the

reaction, indicating that $% crystals do not play a role in the induction periodI+.

"t is now widely accepted that once the pore-solution is saturated, which

generally happens during mixing, the nucleation and growth of $-S-% startsFG,I(.

According to this viewpoint, the induction period is not a separate chemical or

physical process, and is observed because the rate of reaction, albeit accelerating, is

too low to be measurable. This inference is also supported by the fact that

induction period is found to be shorter for finer powders where the reaction in the

third stage is fasterFI,IG.

2./.2 St%0( Acc()(r%ti0 R(%ctio R%t($

"n the third stage the hydration accelerates until a peak is reached. As this

feature is consistently observed in all studies and is, in all certainty, directly linked

to the mechanism of the reaction, the reason for this acceleration has been, and

continues to be, the subect of an extensive debate. The reaction rate and the

17


40/190


position of the peak is known to depend on the temperature and the particle si'es

of $GS

I)

. The rate of reaction is also known to depend on the crystal structure andsurface defects in $GSF+,F(.

"n most of the early work on hydration kinetics, the first four stages of

hydration were explained using separate processesGN,)J,IF. As discussed earlier, 3ondo

and 6edaGN, and Bommersheim and $lifton)J, explained the acceleration in the

reaction rate by the gradual deconsumption of a protective layer that forms early

in the reactionF). hile many recent studies still propose similar mechanisms, no

conclusive evidence to the presence of a protective layer is reported.

"n +J* Tenoutasse and 5e5onderF* suggested that a single mechanism of

nucleation and growth could be used to explain the behaviour observed in stages (

to ). Mne of the reasons for this conclusion was that the Eohnson-0ehl-Avrami-

3olmogorov e#uationII,I,IN,IJ, which models the nucleation and growth of solid

nuclei in a homogeneous fluid medium, can be used to fit the observed rate of

hydration for cement. =ater studies verifying that this e#uation can be used to fit

the rate of hydration in pure-aliteFI,I),* and for Bortland cement+ leant further

credence to the possibility of cement hydration being controlled by a nucleation

and growth mechanism.

The nucleation and growth mechanism is a demand based process and the

rate of the reaction is not limited by the availability of reactants. "n this process,

germs of the product form and start to grow at a rate that is proportional to the

surface area available on these germs. Since these germs can redissolve, they have

to reach a minimum critical si'e over which growth is preferred to dissolution. The

nuclei continue to grow at a rate proportional to their free surface area leading

first to an acceleration in the process, and then a subse#uent deceleration due to

reduction in the available surface area resulting from impingement of neighbouring

nucleiII,I,IN,IJ. This process results in an S-shaped evolution of the reaction similar

to that observed in cement.

1'


41/190


Lased on the nucleation and growth mechanism, it was suggested that a slow

nucleation of $-S-% occurs on the surface of alite particles during the so-calledinduction period. Mnce the nuclei reach a critical si'e the reaction accelerates,

entering the third stageIG,(,G. hile most authors have suggested the formation of a

continuous layer of $-S-% forming over the surface of $GS particlesIG, it was

recognised that increase in the surface area of the particles due to growth of

particles could not account for the increased reaction rate. Studies have suggested

the possibility of discontinuous growth of nuclei on the surface of the particles well

into the third stage of the reactionFG,)

.Apart from slight variations, it is now generally accepted that the nucleation

and growth mechanism is responsible for the observed acceleration in stage three.

The reaction kinetics of alite during the nucleation and growth period are

discussed in more detail in chapter F.

2./. St%0($ / 3 R(duci0 R(%ctio R%t($

"n stage ), the reaction rates slow down to almost half their value #uicklyfollowed by a slower reduction in stage F until most of the $GS or water has been

consumed*. "n most early studies, it was postulated that thickness of hydrates

depositing over the cement particles increases with hydration and the rate of

reaction is controlled by the diffusion of ions through this layer of hydrates.

According to this theory, stage ) occurs when a shift towards a diffusion controlled

mechanism starts and in stage F the reaction is controlled entirely by diffusion and

the availability of materialsGN,F.

Some recent studies have indicated that the nucleation and growth

mechanism can also be used to explain the observed behaviours until a few hours

after the peak),I(. "n these studies, the reduction in the reaction rate is explained

by the reduction in the available surface area for growth due to impingement

between neighbouring nuclei, either from the same particle, or from the

1(


42/190


surrounding particles. "t has also been suggested that as the nucleation and growth

process continues, the surface of the particles gets progressively covered byhydrates, leading to a diffusion controlled regime when the entire surface of the

particles gets coveredI+. %owever, no conclusive evidence of this was found.

Mnly a limited number of studies focussing on these stages of hydration have

been found and the reaction mechanism in these stages is still not clear. "f a

diffusion controlled regime is assumed, the point of transition from the nucleation

and growth mechanism to diffusion controlled kinetics is also not clear.

2.3 A%)&tic%) %d Nu"(ric%) Mod()$ o' H&dr%tio Ki(tic$

2.3.1 Coc(tric Gro4t, Mod()$

3ondo and 6edaGN, and later Bommersheim and $lifton)J,F, explained the

hydration kinetics of alite using mathematical models of suggested mechanisms

acting due to concentric layered growth of hydrates over reacting spherical cement

particles Cfigure (.+*D. "n both these models, an initial layer of meta-stablehydrates forms upon the first contact of cement with water. This Ubarrier-layerV of

early hydrates slows down the reaction, leading to the so-called Uinduction periodV.

This layer dissolves or becomes more permeable with time leading to an

acceleration in the reaction rate.

20

Figure 2.1(: Schematic re,resentation of h$drating C ) S grain in concentric gro#th modelsb$ 8ondo and 9eda )6 %left& and Pommersheim and Clifton 7 %right&


43/190


ith hydration the reacting core of the particle reduces and is replaced by an

inner hydration product, which grows inwards from the original Ubarrier-layerV.Mutside this layer an outer hydration product grows outwards into the capillary

pore-space. Mnce the cover of hydrates around the particles reaches a certain

thickness, the resistance offered to the reacting ions becomes sufficiently high to

control the rate of the reaction, and the reaction shifts to a diffusion controlled

regime. The relations used by the authors of these models can be found in the

original works referred to above. Since each mechanism uses a different e#uation,

the relation that predicts the slowest reaction rate any any instant in time ischosen as the governing mechanism.

Although these and other similar models were used to explain the hydration

kinetics of alite for many years, experimental observations did not show the

presence of a protective Ubarrier-layerV during the induction period or afterwards.

Since the presence of this layer is crucial to the validity of these models, the

validity of these models is often #uestioned. %owever, the idea of spherical cement

particles with concentric growth of hydrates is still widely used to model variousphenomena.

!arious other simple mathematical relations have been developed to model

chemical processes using the assumption of a spherical reaction front. hile most

of these models were developed for systems other than cement, they have been

widely used to model cement hydration. &or example, one such sigmoid relation,

which was developed by EanderI for solid state reactions, has been used in various

forms to fit the early evolution of hydrationGN,I). Mne of the fre#uently used forms of

this e#uation is shown in e#uation (.G.

r =+−+− kt r G

C(.GD

21


44/190

Analytical and Numerical Models of Hydration inetics

"n this e#uation W is the degree of hydration, t the time, k is the rate constant

and r the radius of the particle. This e#uation models the formation of athickening diffusion barrier on the reaction surfaces that slows down the reactions.

Kinstling and Lrounshtein derived another expression to account for the

reduction in the interfacial area between the reactants and the products Ce#. (.)D.

+−(G−+−

(G=

kt

r (C(.)D

A problem with using these relations with cement is that while most of these

relations are derived for a single particle or for a powder with particles of the same

si'e, cement is composed of particles of a wide range of si'es and these relations

may therefore not be applicable to cementIF,N. "n the models that choose between

multiple mechanisms, such as the Bommersheim and $lifton model discussed

above, the switch between different regimes could take place at different moments

for different particles, which cannot be accounted for in single particle models.

These relations could still be applied to polydisperse powders by adding the effect

of individual particle si'es and it was also shown that the fit parameters in this

case are not the same as in the case when the fits are made assuming a single

averaged particle si'eI).

1elations modelling similar mechanisms to explicitly consider the effect of

different particle si'es have also been developed specially for cementJ,N*,N+,N(. hile

these relations provided insight about hydration, since each e#uation is dedicated

to a single hypothesised mechanism for which it is derived, the derivation, and

even the use, of these relations may be cumbersome. 0oreover, while these

relations can be useful in studying systems where the reaction mechanism is

understood, a good fit of experimental data with these e#uations does not

necessarily mean that the mechanisms being studied are similar to those assumed

for the derivation of the e#uation. "n fact most sigmoid e#uations with sufficient

number of parameters can be fit to cement hydration.

22


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2.3.2 T,( 5o,$o-M(,)-A+r%"i-Ko)"o0oro+ E6u%tio

The Eohnson-0ehl-Avrami-3olmogorov e#uationII,I,IN

, more commonlyreferred to as the Avrami e#uation, was originally empirically derived by Austin

and 1ickett to model the decomposition of austeniteIJ. The later derivations of the

e#uation modelled the rate of phase change in solidifying metal melts. Although

this e#uation could also be considered a concentric growth model, it is being

considered separately here because of its fre#uent use in cement. This e#uation

models the nucleation and growth process, where small nuclei of the product form

at random locations in the pore-space and grow to overlap and form a solidskeleton, at constant rates on all available surfaces. "n the derivation, spherical

isotropic growth of the nuclei is assumed, and the reduction in the surface area due

to overlaps between neighbouring nuclei is accounted for statistically.

The most commonly used form of this e#uation is shown in e#uation (.F,

where is the degree of phase change, t the time, and k and n are parameters that

depend on the rate of reaction and the mechanism of growth of crystals

respectively.

−ln+−=kt n C(.FD

23

Figure 2.11: Schematics of overla,,ing s,herical grains from Avrami 0!


46/190


hile this e#uation has often been erroneously used for systems with varying

temperature, it is only applicable to isothermal systems. To study the rates ofreactions, the e#uation can be differentiated to the form in e#uation (.I.

d

d t =knt n −+e −kt

n

C(.ID

Although in the original theory, n was defined to be an integer between +

and ), it was found that the value of n may be non-integralNG,N). =ater, the

parameter n was further defined in terms of three other parameters, P , S and ; as

shown in e#uation (..

n = P S ; C(.D"n this e#uation P is a dimensionality constant for the growth of products,

being + for a one-dimensional growth, ( for a two-dimensional growth and G for a

three-dimensional growth. S is related to the rate-limiting mechanism, being + for

interface controlled growth, where the creation of new surface controls the rate,

and ( for cases where the diffusion of ions to the growth sites controls the rate. ;

depends on the nucleation rate, being + for a constant nucleation rate and * for

cases where only an initial nucleation event occursFI. This means that as long as

the mechanism of a reaction remains the same, the value of n should stay constant

for a reaction.

Tenoutasse and 5e5onderF* reported the first use of this e#uation to model

cement hydration. 0any researchers have since reported good fits of the e#uationwith experimental resultsFI,I),*,+ and the Avrami e#uation has become the most

widely accepted relation used to model the early-age hydration kinetics of cement.

"n the Avrami e#uation, the parameter k is a combined rate constant that

can depend on many factors such as the rate of nucleation and the rate of growth,

the diffusion in solution and the temperature of the system. "n the case of cement,

24


47/190


this factor can depend on the temperature, the state of the pore-solution and the

specific surface, and hence by extension the particle si'e distribution, of thecement, amongst other factors. Although some studies assumed a negligible effect

of particle si'e distribution on hydrationNF, it is generally accepted that the fit

value of k in the Avrami e#uation is found to be higher for finer cements I),N, which

directly follows from the fact that finer cements exhibit higher reaction rates.

%owever, a relation linking the variation of k to the particle si'e distribution or the

specific surface area of cement can not be found in the literature.

Although the value of n in the Avrami e#uation should depend only on thereaction mechanism, wide discrepancies in reported values for cement and alite

hydration can be found in the literature. hile in the original application of the

e#uation by Tenoutasse and 5e5onderF*, G was found to be an acceptable value for

n, later studies found n to vary between ( and GFI,*,NI. 2arlier, Le'ak and EelenikI)

had suggested that the lower observed values of n could be due to

misinterpretation of the Avrami parameters for poly-si'ed cement specimens. They

pointed out that, in a poly-si'ed cement specimen, particles of different si'es reacttogether and are at different stages of the reaction at any moment in time. This

results in an overall behaviour that is a mixture of the overlapping of hydration

mechanisms, making the interpretation of the Avrami parameters difficult.

$onse#uently, the observed value of n could also result from a combination of

different mechanisms acting together.

The use of the Avrami e#uation in cement has often been criticised. Mne of

the important criticisms arising from the above discussion is that the use of this

e#uation usually becomes only a fitting exercise, and the relationship between the

fit-parameters and the material properties or the reaction mechanism is not clear.

"t has also been shown that the fits are not sensitive to the value of n and that

with a variation in n , the data can still be fit by varying k *. The fits do not

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provide any additional information than what can be obtained ust by plotting the

experimental results.Another serious criticism to the Avrami e#uation is that while this e#uation

was derived for systems where nucleation occurs at homogeneously distributed

random locations in the system, in the case of cement it is known that the

nucleation occurs heterogeneously, only on the surface of the particlesF*,*,). "t was

recently shown that a relation derived for cases where the nucleation is assumed to

occur on a boundaryN gives better fits to heat-evolution curves from cement

hydrationI(.

5espite serious reasons for the Avrami e#uation not being applicable to

cement, it is currently the most widely used e#uation to fit hydration-rates. This is

probably owing to the simple form of the e#uation and that it only has two fit

parameters. hile these two parameters may not be sufficient to capture all the

factors at play during cement hydration, they provide a simple means to compare

different systems. Still, good fits with these e#uations do not necessarily imply that

the actual mechanism in cement is similar to that modelled in the e#uation.

2.3. T,( Di7o Nu"(ric%) Mod() 'or 8oud%r& Nuc)(%tio

"n order to better reproduce the conditions in real cements, Karrault and

/onatFG developed a numerical model to simulate the growth of $-S-% nuclei on

the surface of $GS particles. "n this model, nuclei of $-S-% form on a two-

dimensional surface with periodic-boundary conditions to simulate closed

continuous surfaces. At each step in the simulation, the nuclei grow both parallel

and perpendicular to the surface. "t was observed that good fits with experimental

results can be obtained if the perpendicular growth rate is assumed to be higher

than the parallel growth rate. The growth is simulated by generation of new $-S-%

elements on the boundaries of the $-S-% elements already present on the surface.

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The vertical growth is obtained by duplicating the $-S-% layers in the vertical

direction.

The physics of this model have been based on A&0 images that show an

aggregation of nanometric thin $-S-% particles of similar si'es on the surface of

$GS particlesFG,NN. "n order to obtain the values of the perpendicular and the parallel

growth rates under different conditions, the model has been calibrated withexperimental results obtained from hydration of alite particles in dilute lime

solutions of different concentrations, where the rate of hydration and the

concentration of the solutions was measured.

"n this model, the induction period is modelled as the time taken for the

formation of the nuclei, and the following acceleration results from the continuous

increase in the surface available for growth. As the nuclei on the surface continue

to grow they start to impinge on each other, reducing the surface for growth andhence the rate of hydration. This model predicts that in the early hours of the

hydration, the surface of cement particles is only partially covered by hydrates and

gets fully covered by hydrates after the peak of hydration.

"t can be shown that if the Avrami e#uation is used to model the fraction of

the surface covered at any moment in time, which is an example of homogeneous

27

Figure 2.12: Schematics of the nucleation and gro#th im,lemented in the i


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nucleation in two-dimensions, the volume of product C= D on the surface can be

written as e#uation (.N where A is the surface area of the particle, k ,ar the parallelgrowth rate constant, k ,er, the perpendicular growth rate and t the time.

= =A⋅+−exp−k ,ar ⋅t (⋅k ,er,⋅t C(.ND

Mne of the critical drawbacks of this approach is that while the growth of

nuclei is considered explicitly, the effect of inter-particle interaction is not

considered. Since the setting of cement can mechanically occur only when the

hydrates start to bind the particles together, the interaction between the hydration

products from different particles starts before the set. "n this model, although the

reaction rate is modelled until times well beyond the observed setting times of

normal cement, the interaction between different particles cannot be considered in

the numerical system used in this model. Still, this model provides important

information about cement hydration as the parameters obtained from this model

are able to predict reaction rates in systems that are significantly different from

those used for calibration.

2.9 Su""%r& o' C("(t H&dr%tio %d Out$t%di0

:u($tio$

"t can be seen from the above discussion that while tremendous progress in

understanding cement has been made, many outstanding #uestions remain. "n this

section, the aspects of our knowledge relevant to this study and the pertaining

#uestions are discussed. Since the current study focusses on alite, the discussion is

limited to the points relevant to alite.

Although most of the reactant and product phases in alite hydration are

known, discrepancies in the chemical composition of $-S-% exist. hile the

properties exhibited by cement indicate complexity in its structure, an accurate

model of $-S-% structure is not available and descriptions of the product vary

from colloidal to fibrillar. &ibres or suspension of fibres of $-S-% can be often

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observed in micrographs, but the observations are at times inconsistent. As

samples are dried before observation, the microstructure of the samples could bealtered and the morphology of $-S-% is still not well understood. The density of $-

S-% has been shown to vary and the exact range of this variation is not known.

The fibres observed in micrographs could indicate the variation of the density over

a wide range.

2ven though the presence of empty hollow shells around cement particles has

been widely accepted, recent results show that the shells are not empty and are

filled with a low density product. This observation is contrary to the belief thatthe inner product is always Uhigh-densityV.

$ompared to $-S-%, $% displays more consistent properties, but it hasnt

been as extensively studied as $-S-%. The shape and si'e of $% crystals is known

to vary, but their relationship with various controlling factors is not well

understood. An early idea that portlandite might play an important role in

reaction kinetics was later reected.

hile the hydration mechanism during the induction period is still not clear,

it is generally agreed that the nucleation and growth of $-S-% controls the

hydration kinetics. /ucleation and growth is a physical process depending on the

shape and dispersion of a phase and proper understanding of the kinetics would

re#uire a better knowledge of the morphology of $-S-%.

The hydration mechanism after the peak of hydration and the point of shift

from the nucleation and growth regime to a diffusion controlled regime is also notclear. 5ata concerning the post-peak hydration is limited and it is generally

assumed that hydration peaks due to a shift to a diffusion controlled mechanism.

%owever, the disperse nature of $-S-% observed in micrographs suggests high

permeability for fluids and ions. Studies have also shown the possibility of the

nucleation and growth mechanism explaining the post-peak behaviour.

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hile this relationship might hold for one particular type of mix, it would be

a gross generalisation to assume that the changes in arrangement and structure of

porosity and the microstructure do not have a role to play. &igure (.+), which

compares the variation of compressive strength with porosity against Lalshin:sNJ

model for different systemsJ(, clearly shows that a mortar mix can have twice as

31

Figure 2.1: *>,erimental scatter of com,ressive strengths of different s$stems against?alshin5s model 72

Figure 2.1): elationshi, of com,ressive strength #ith gel-s,ace ratio %after Po#ers17/6 7 &


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Modelling Cement Hydration

much mechanical strength for the same porosity, clearly demonstrating the

importance of accounting for microstructure and not ust the total porosity in thecalculation of mechanical properties.

"n recent years an increasing emphasis is being laid on durability based

design. ith the demands on concrete structures increasing rapidly, problems like

corrosion, ion transport and other long term effects have gained focus in many

studies and porosity and pore-connectivity have been found to be important

parameters controlling deterioration. Since most of these effects are long term, only

accelerated tests, whose accuracy is fre#uently #uestioned, a

vector modelling of hydrating cement microstructure and kinetics cement.pdf

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